The sum of two numbers is 76 and their difference is 52. Find the two numbers. Please explain

Please help I need help

navik [9.2K]

Answer:

L=10pi, or 31.42

Step-by-step explanation:

4 0

2 years ago

Iron Man Training While training for an iron man competition, Tony bikes for 60 miles and runs for 15 miles. If his bikes speed

ivolga24 [154]

Answer:

Tony biked 1 hour 40 minutes and run 3 hours 20 minutes.

Step-by-step explanation:

How long did Tony speed on his bike?

Let s to be Tony's running speed, then 8s is Tony's biking speed

Let's recall that Time = Distance/Speed

Bike time + Running time = 5 hrs

Replacing with the real values, we have:

60/8s + 15/s = 5

8s as Lowest Common Denominator

60 + 8 * 15 = 5 * 8s

60 + 120 = 40s

-40s = -180

s = -180-40

s = 4.5 ⇒ 8s = 36

Tony run at 4.5 mph and biked at 36 mph

Now, we can calculate the time, this way:

Bike time = Bike distance/Bike speed

Replacing with the real values, we have:

Bike time = 60/36

Bike time = 5/3 (Dividing by 12)

5/3 hours * 60 = 100 minutes or 1 hour 40 minutes

Running time = 5 hours - 1 hour 40 minutes = 3 hours 20 minutes

Tony biked 1 hour 40 minutes and run 3 hours 20 minutes.

4 0

3 years ago

The average test scores for a particular test in algebra was 84 with a standard deviation of 5. What percentage of the students

Delicious77 [7]

Answer:

The percentage of the students scored higher than 89% is 15.87%

Step-by-step explanation:

we are given

The average test scores for a particular test in algebra was 84

so, mean is 84

$\mu=84$

a standard deviation of 5

so,

$\sigma=5$

we have

x=89

now, we can use z-score formula

$z=\frac{x-\mu}{\sigma}$

now, we can plug values

$z=\frac{89-84}{5}$

$z=1$

now, we can use calculator

and we get

$p(z>1)=0.1587$

So,

The percentage of the students scored higher than 89% is 15.87%

8 0

3 years ago

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves

Vadim26 [7]

The expression on the left side describes a parabola. Factorize it to determine where it crosses the y-axis (i.e. the line x = 0) :

-3y² + 9y - 6 = -3 (y² - 3y + 2)

… = -3 (y - 1) (y - 2) = 0

⇒ y = 1 or y = 2

Also, complete the square to determine the vertex of the parabola:

-3y² + 9y - 6 = -3 (y² - 3y) - 6

… = -3 (y² - 3y + 9/4 - 9/4) - 6

… = -3 (y² - 2•3/2 y + (3/2)²) + 27/4 - 6

… = -3 (y - 3/2)² + 3/4

⇒ vertex at (x, y) = (3/4, 3/2)

I've attached a sketch of the curve along with one of the shells that make up the solid. For some value of x in the interval 0 ≤ x ≤ 3/4, each cylindrical shell has

radius = x

height = y⁺ - y⁻

where y⁺ refers to the half of the parabola above the line y = 3/2, and y⁻ is the lower half. These halves are functions of x that we obtain from its equation by solving for y :

x = -3y² + 9y - 6

x = -3 (y - 3/2)² + 3/4

x - 3/4 = -3 (y - 3/2)²

-x/3 + 1/4 = (y - 3/2)²

± √(1/4 - x/3) = y - 3/2

y = 3/2 ± √(1/4 - x/3)

y⁺ and y⁻ are the solutions with the positive and negative square roots, respectively, so each shell has height

(3/2 + √(1/4 - x/3)) - (3/2 - √(1/4 - x/3)) = 2 √(1/4 - x/3)

Now set up the integral and compute the volume.

$\displaystyle 2\pi \int_{x=0}^{x=3/4} 2x \sqrt{\frac14 - \frac x3} \, dx$

Substitute u = 1/4 - x/3, so x = 3/4 - 3u and dx = -3 du.

$\displaystyle 2\pi \int_{u=1/4-0/3}^{u=1/4-(3/4)/3} 2\left(\frac34 - 3u\right) \sqrt{u} \left(-3 \, du\right)$

$\displaystyle -12\pi \int_{u=1/4}^{u=0} \left(\frac34 - 3u\right) \sqrt{u} \, du$

$\displaystyle 12\pi \int_{u=0}^{u=1/4} \left(\frac34 u^{1/2} - 3u^{3/2}\right) \, du$

$\displaystyle 12\pi \left(\frac34\cdot\frac23 u^{3/2} - 3\cdot\frac25u^{5/2}\right) \bigg|_{u=0}^{u=1/4}$

$\displaystyle 12\pi \left(\frac12 u^{3/2} - \frac65u^{5/2}\right) \bigg|_{u=0}^{u=1/4}$

$\displaystyle 12\pi \left(\frac12 \left(\frac14\right)^{3/2} - \frac65\left(\frac14\right)^{5/2}\right) - 12\pi (0 - 0)$

$\displaystyle 12\pi \left(\frac1{16} - \frac3{80}\right) = \frac{12\pi}{40} = \boxed{\frac{3\pi}{10}}$

6 0

2 years ago

If 15 mi = 8 km, about how many miles would be equal to 50 km?

Anon25 [30]

Use ratios to solve

15 m/8 km = x m/50 km Cross multiply
15(50) = 8x
750 = 8x divide by 8 on both sides
93.75 = x

93.75 miles = 50km

6 0

3 years ago