What is the answer to this question ?
If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) g(1) = 4 h(1) = 7 g' (1) = 5 h' (1) = −3 fx(4, 7) = 4 fy(4, 7) = 7 find dz/dt when t = 1.
The derivative of z with respect to t (dz/dt) when t=1 is -1 using the chain rule for multivariable functions.
Explanation:This problem uses the chain rule for multivariable functions. Given that z = f(x, y) where x = g(t) and y = h(t), to find dz/dt when t = 1, we apply the chain rule as follows: dz/dt=∂f/∂x *(dx/dt)+ ∂f/∂y * (dy/dt). Here, we have x=g(t), y=h(t), ∂f/∂x = fx(4, 7) = 4, ∂f/∂y = fy(4, 7) = 7, dx/dt = g'(1) = 5, and dy/dt = h'(1) = -3.
Substituting these values in: dz/dt = 4 * 5 + 7 * (-3) = 20 - 21 = -1. Therefore, dz/dt = -1 when t = 1.
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How many yards equals 765 inches?
Enter your answer, as a decimal.
A stone is thrown straight up from the edge of a roof, 675 feet above the ground, at a speed of 16 feet per second. A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 3 seconds later?
Final answer:
The stone would be 579 feet high after 3 seconds.
Explanation:
To calculate the height of the stone 3 seconds later, we can use the kinematic equation for position:
h = h0 + (v0 · t) + ((1/2) · a · t2)
where:
h is the final height
h0 = 675 feet is the initial height
v0 = 16 ft/s is the initial velocity
t = 3 seconds is the time
a = -32 ft/s2 is the acceleration due to gravity
Let's plug in the values and calculate:
h = 675 + (16 · 3) + ((1/2) · (-32) · 32)
Solving this equation, we get:
h = 675 + 48 - 144
h = 579 feet
what is 1/6 divided by 4/7 then that answer simplified
The value of the equation after the division and simplification is A = 7/24 or A = 0.291667
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first fraction be p = 1/6
Let the second fraction be q = 4/7
Now , the equation is A = p/q
On dividing the terms p and q , we get
Substituting the values in the equation , we get
A = ( 1/6 ) / ( 4/7 )
On simplifying the equation , we get
A = ( 1/6 ) x ( 7/4 )
A = 7/24
So , the value of A after division is
Now , on further simplification , we get
A = 0.291667
Hence , the equation after simplification is A = 0.291667
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Andrew make six dollars an hour +9 dollars an hour for every hour of overtime overtime hours or any hours more than 40 hours for the week create an equation that shows amount of wages earned for working x hours no overtime
Three weeks ago John bought stock at 49 ¼; today the stock is valued at 49 7/8. We could say the stock is performing at which of the following? A. Above par B. Par equality C. On par D. Below par
The base of a triangle is 7 inches more than its height. If the area of the triangle is 60 square inches, find the base and height of the triangle.
Let x be the total number of customers in a one-hour interval and y be the total number of female customers in the same interval. find the joint pmf of x and y.
The joint PMF of X and Y is [tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \cdot \frac{x!}{y!(x-y)!} \cdot \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad \text{for } y = 0, 1, \ldots, x \text{ and } x = 0, 1, 2, \ldots[/tex]
Distributions of X and Y
X is the total number of customers visiting the store in an hour, which follows a Poisson distribution with mean [tex]\lambda = 10[/tex]
[tex]P(X = x) = \frac{e^{-10} \cdot 10^x}{x!}, \quad x = 0, 1, 2, \ldots[/tex]
Given X = x the number of female customers Y follows a binomial distribution because each customer is independently female with probability [tex]p = \frac{3}{4}[/tex]
[tex]P(Y = y \mid X = x) = \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}, \quad y = 0, 1, \ldots, x[/tex]
Joint PMF of X and Y
To find the joint PMF P(X = x, Y = y, we use the law of total probability:
[tex]P(X = x, Y = y) = P(Y = y \mid X = x) \cdot P(X = x)[/tex]
Substitute the expressions for [tex]P(Y = y \mid X = x)[/tex] and P(X = x)
[tex]P(X = x, Y = y) = \left( \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y} \right) \cdot \left( \frac{e^{-10} \cdot 10^x}{x!} \right)[/tex]
Simplify the expression:
[tex]P(X = x, Y = y) = \frac{e^{-10} \cdot 10^x}{x!} \binom{x}{y} \left(\frac{3}{4}\right)^y \left(\frac{1}{4}\right)^{x-y}.[/tex]
Lim x → 2 (x3 − 3x + 3) = 5 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1
A greeting card company can sell cards for $2.75 each, so the revenue can be calculated using the formula 2.75 Rx . The company’s total cost consists of a fixed overhead of $12,000 plus 35 cents per card, so the total cost can be calculated using the formula 0.35 12000 Cx .
a. Write the algebraic equation needed to determine when the company will break even (when the revenue will equal the cost).
b. Solve the equation from part a.
c. Write the algebraic inequality needed to indicate that the revenue is greater than the cost.
d. Solve the inequality from part c.
e. What does your answer from part d tell you about when the company will make a profit?
53 freshman were interviewed about the classes they were taking this semester 24 said they were taking science 22 said they were taking math 17 said they were taking English 7 said they were taking both science and math 10 said they were taking both math and English 4 said they were taking both math and English 2 said they were taking all three classes
The questions are:
How many students are not taking any science, math, or English? ANDThis is best answered using a Venn diagram. If you look at the separate areas, you see there are 7 areas.
The common area is the two students who takes the three classes.
4 said they were taking both math and English
4 – 2 = 2 only take math & English
7 said they were taking both science and math
7 – 2 = 5 only take math and science
10 said they were taking both science and English
10 – 2 = 8 only take science and English
17 said they were taking English
17 – (2 + 8 + 2) = 5 take only English
22 said they were taking math
22 – (2 + 5 + 2) = 13 take math
24 said they were taking science
24 – (2 + 8 + 5) = 9 only take science
Adding them all up:
2 + 9 + 13 + 5 + 8 + 5 + 2 = 44
So, 44 students are taking the 3 courses
53 – 44 = 9 students are not taking any of the 3 courses
5 + 13 + 9 = 27 take only 1 of these courses
The formula A=P(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate.
Solve for r.
Answer: [tex]r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex]
Step-by-step explanation
Compound interest is the addition of interest to the principal sum of a deposit or a loan.
Let P = principal amount which was taken as a loan then the accumulated amount A is given by
[tex]A=P(1+r)^t[/tex].......(1)
where, r is the rate of simple annual interest in decimal.
t is the time applied for interest.
For solving r divide both sides of equation by P in (1),we get
[tex]\frac{A}{P}=(1+r)^t\\\Rightarrow(\frac{A}{P})^{\frac{1}{t}}=1+r\\\Rightarrow\ r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex].
Ajax buys 20 shares of stock at 20$ per share. The shares increase in value by 20%. He then sells 10 shares. After the shares decrease in value by 10%, he buys another 20 shares. The shares then all increase by 50%. Determine the total dollar value of the 30 shares that Ajax now owns.
Answer:
$972
Step-by-step explanation:
Ajax buys 20 shares of stock at $20.
The cost of 20 shares = 20 × $20 = $400
The shares increase in value by 20%
Now the cost of 20 shares = 400 + (20%×400)
= 400 + 80
= $480
Cost per share = [tex]\frac{480}{20}[/tex] = $24
He sells 10 shares = $20 × 10 = $240
Now he has 10 share costs $240
After the shares decrease in value by 10%, he buys another 20 shares.
Cost per shares after decrease by 10% = 24 - (10%×24)
= 24 - 2.40
= $21.60
He buys 20 shares and his remaining 10 shares = 20 + 10 = 30 shares
Cost of 30 shares = 21.60 × 30 = $648
The shares then all increase by 50% = 648 + (50% × 648)
= 648 + (0.5 × 648)
= 648 + 324
= $972
The total value of the 30 shares that Ajax own is $972
Write an equation for the translation of y = |x| and the translation is up 4 right 2.
Nick has $7.00. Bagels cost $0.75 each, and a small container of cream cheese costs $1.29. Write an inequality to find the numbers of bagels Nick can buy.
let x = bagels
0.75x +1.29 <= 7.00
solve:
0.75x +1.29<=7.00
0.75x <= 7.00 - 1.29
0.75x <=5.71
5.71 /0.75 = 7.6
x<=7 bagels
A playground has two poles that are used for games. The first pole is 1.83 m tall. The second pole is 2.172 m tall.
How much taller is the second pole than the first pole?
Enter your answer in the box.
pls help, will matrk brainliest
Answer:
mark me brainliest plz im a beginner and the answer is .342 becuase the m ok lo, xd
Step-by-step explanation:
A trampoline cost $220 and the sales tax is 6.25% what is the total cost of the trampoline
Answer:
$233.75Step-by-step explanation:
You purchased 8 pounds 10 ounces of candy from a candy shop. You want to split it equally among 3 classrooms at a local school./7425116/3d9f02b9?utm_source=registration
If <0 <90 and cos0=11/15 what is the value of sin (90-0)
Marks brothers is paying a dividend of 56.25 on each share how much will PRH receive in dividends
To calculate the total dividend PRH will receive, multiply the dividend per share by the number of shares PRH owns.
Explanation:To calculate how much PRH will receive in dividends, we need to know the number of shares PRH owns. Let's assume PRH owns X number of shares. We can multiply the dividend of $56.25 per share by the number of shares to find the total dividend PRH will receive.
Total Dividend = $56.25 x X
For example, if PRH owns 100 shares, the total dividend will be $56.25 x 100 = $5625.
Without knowing the number of shares PRH owns, we cannot calculate the total dividend payment. With the number of shares, multiply by the dividend per share ($56.25) to get the total dividends. For present value calculations, divide the PDV of profits by the number of shares to get the price per share.
Explanation:To determine how much PRH will receive in dividends from Marks Brothers, a specific number of shares owned by PRH would be needed. Without this information, we cannot calculate the exact dividend payment to PRH. However, if we had the number of shares, we would multiply that number by the dividend per share, which is $56.25, to find the total dividend payment PRH would receive.
For example, if PRH owns 10 shares, the calculation would be 10 shares × $56.25 per share = $562.50 in total dividends. To understand the calculations surrounding the present value or PDV, consider that a different PDV calculation needs to be done for amounts received at different times. Once the PDV of total profits is calculated, it can be divided by the number of shares to find the price per share. Using the provided example with a total PDV of profits being $51.3 million and 200 shares, the calculation would be $51.3 million / 200 = 0.2565 million or $256,500 per share.
Note that in the real world, expected profits are estimates rather than exact figures, and determining an accurate interest rate is part of that estimation process.
which of the following is equal to (2x/5-9 )+9
a.2x/5
b.5x/2
c.2x-45/5
d. (2x-9)+45
Is -2x+3y=6 parallel, perpendicular, or the same line as 2x-3y=9?
whats the slope of (-3,-2) and (5,4)
Determine the slope and y-intercept of the line. y = 8.5x + 6
Answer: Slope = 8.5 and y-intercept = 6
Step-by-step explanation:
The intercept form of a linear equation is given by :_
[tex]y=mx+c[/tex], where m( coefficinet of x ) is the slope and c (constant term) is the y-intercept.
The given equation in intercept form : [tex]y = 8.5x + 6[/tex]
Here , the coefficient of c = 8.5
thus , the slope = 8.5
Also, the constant term = 6
Thus, the y-intercept =6
You have just arranged for a $1,640,000 mortgage to finance the purchase of a large tract of land. the mortgage has an apr of 6.4 percent, and it calls for monthly payments over the next 30 years. however, the loan has an eight-year balloon payment, meaning that the loan must be paid off then. how big will the balloon payment be?
The balloon payment is approximately $1,084,898.37.
To calculate the balloon payment, we first need to determine the remaining balance of the mortgage after the initial 22 years of payments (30 years total - 8 years).
Step 1: Calculate the monthly interest rate.
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 6.4% / 12 = 0.00533
Step 2: Calculate the number of payments made in 22 years.
Number of payments = 22 years * 12 months/year = 264 payments
Step 3: Use the formula for the remaining balance of a mortgage.
Remaining balance = [tex]P * [(1 + r)^n - (1 + r)^t] / [(1 + r)^n - 1][/tex]
Where:
P = principal amount of the loan
r = monthly interest rate
n = total number of payments
t = number of payments already made
Substitute the given values into the formula:
Remaining balance = $1,640,000 * [(1 + 0.00533)^360 - (1 + 0.00533)^264] / [(1 + 0.00533)^360 - 1]
Remaining balance = $1,084,898.37
The balloon payment is the remaining balance after 22 years. Therefore, the balloon payment is approximately $1,084,898.37.
If 21–(a–b)=2(b+9), and a=8, what is the value of b?
Jack has 5 craft sticks he needs four times that number for a project how many craft sticks does Jack need all together
Solving this problem simply only requires us the knowledge of multiplication.
So we are initially given that there are 5 craft sticks. So if we need four times that amount, that is written as:
5 x 4
Which is equal to 20
So Jack needs 20
Please help guys im stuck. THanks
Angle 3 = 70 ( opposite angles equal each other)
Angle 1 = 90-70 = 20 ( angle 1 plus 70 = 90 )
angle 3 - angle 1 = 70 -20 = 50
Answer is B
1 mile is equal to 5280 feet. You've walk 0.20 mile on a track. How many feet have you watched?