How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between x=1 and x=b is equal to 240?

Answer:

[tex]x=31.51\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle

[tex]tan(42\°)=x/35[/tex]

isolate the variable x

[tex]x=35tan(42\°)=31.51\ units[/tex]

angle 4 is the same as angle 8

 angle 7 & angle 8 has to equal 180 degree

 so angle 7 and angle 4 also have to equal 180

angle 4 is 3 times the size of 7

lets call 7  (x)

so 4(x) = 180

180/4  =45

x=45

angle 7 is 45 degrees

Answer: Weight of the oil is 672.74 grams.

Step-by-step explanation:

Since we have given that

Radius of cylinder = 5 cm

Height of cylinder = 10 cm

Volume of cylinder would be

[tex]\pi r^2h\\\\=3.14\times 5\times 5\times 10\\\\=785\ cm^3[/tex]

Weight of 10W-40 oil = 0.857 grams per cubic cm

So, Weight of the oil in the can would be

Volume × Weight per cm³

[tex]=785.71\times 0.857\\\\=672.74\ grams[/tex]

Hence, Weight of the oil is 672.74 grams.

Answer:

Glide reflection

Step-by-step explanation:

A glide reflection is a composition of a translation and a reflection across a line parallel to the direction of translation. A glide reflection requires a translation on a figure, which is then reflected over a line. This is a symmetry operation that requires a translation rule and a line to reflect over. A common example of this are footsteps in the sand.

Answer:

May be !

i> Q = 7P

ii> when p =5 then from above eqn we can find Q = 7p and = 7×5=35

iii> from eqn i we can write p = Q/7 So when Q=42 then P=Q/7=42/7=6

7/10-1/5 = 7/10-2/10 = 5/10 = 1/2

 so 280 pennies fills 1/2 of her piggy bank

 so 280*2 = 560

her piggy bank can hold 560 pennies

Answer: 40 inches squared

Step-by-step explanation:

1. first, you multiply, do 5*16 what does that give you? (80)

2. then, divide your answer by 2 what do you get? (40)

3. lastly, it should look like this: 5*16=(answer)/2=(answer)

hope this helps

Final answer:

The probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%, calculated using the Central Limit Theorem to find the standard error and z-scores.

Explanation:

To calculate the probability that the sample mean diameter of the tennis balls is between 2.62 and 2.64 inches, we can use the Central Limit Theorem since we are dealing with a sample of tennis balls rather than just one. The Central Limit Theorem tells us that the sampling distribution of the sample mean will be normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is called the standard error (SE).

Given that the population mean (μ) is 2.63 inches, the population standard deviation (σ) is 0.03 inch, and the sample size (n) is 9, we first calculate the standard error (SE) as follows:

SE = σ / √n = 0.03 / √9 = 0.03 / 3 = 0.01 inch.

Next, we convert the sample mean range (2.62, 2.64) to z-scores, which are measures of how many standard deviations an element is from the mean.

Z for 2.62 = (2.62 - μ) / SE = (2.62 - 2.63) / 0.01 = -0.01 / 0.01 = -1
Z for 2.64 = (2.64 - μ) / SE = (2.64 - 2.63) / 0.01 = 0.01 / 0.01 = 1

Using a standard normal distribution table or calculator, we find the probabilities corresponding to these z-scores. The probability of a z-score being between -1 and 1 is approximately 0.6827 (68.27%).

Therefore, the probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%.

volume = pi x r^2 x h

3.14 x 4 x 14^2 = 2461.76 cubic feet

Fixed the typo I had in my answer.

Answer:

So volume of the swimming pool is 2461.76 feet³.

Step-by-step explanation:

The Darnells are having a swimming pool installed.

The pool has a radius of 14 feet and height of 4 feet.

Since pool is in the form of a cylinder so volume of cylinder

= πr²h

= π (14)² × 4

= (3.14) (196) × 4

= 2461.76 cubic feet.

So volume of the swimming pool is 2461.76 feet³.

Final answer:

The expression 2(f^4)^2 f^3 divided by 6f^9 simplifies to 1/3 f^2, after applying the properties of exponents and dividing coefficients.

Explanation:

To simplify the expression 2(f^4)^2 f^3 divided by 6f^9, we need to use the properties of exponents. First, we simplify (f^4)^2 by multiplying the exponents, which gives us f^8.

Then, we multiply f^8 by f^3 to get f^11. Next, we divide our new expression 2f^11 by 6f^9. This can be done by dividing the coefficients (2 divided by 6) and subtracting the exponents of f (11 minus 9), resulting in f^2 over 3, or 1/3 f^2.

Answer: [tex]250\ m[/tex]

Step-by-step explanation:

Assuming that:

[tex]1\ m=3.3\ ft[/tex]

We can make the conversion from feet per second to meters per second with this procedure:

[tex](165\ \frac{ft}{s})(\frac{1\ m}{3.3\ ft})=50\ \frac{m}{s}[/tex]

Let be "x" the amount of meters the parachutist will fall during 5 seconds of free fall

Knowing that in 1 second the parachutist falls 50 meters, we can calculate "x" by solving the following multiplication:

[tex]x=(50\ \frac{m}{s})(5\ s)\\\\x=250\ m[/tex]

The parachutist's rate of free fall is 165 feet per second, which is equivalent to 50 meters per second. The parachutist will fall approximately 250 meters during 5 seconds of free fall.

To convert the rate of 165 feet per second to meters per second, we need to use the conversion factor of 1 meter equals 3.3 feet. So, the rate in meters per second is 165 feet per second divided by 3.3 feet per meter, which equals 50 meters per second.

To find how many meters the parachutist will fall during 5 seconds of free fall, we can multiply the rate of 50 meters per second by the time of 5 seconds. This gives us 250 meters of free fall during 5 seconds.