Answer:
<u>It</u><u> </u><u>is</u><u> </u><u>c</u><u>:</u><u> </u><u>1</u><u>5</u><u>.</u><u>6</u><u>2</u><u>5</u><u> </u><u>cm³</u>
Step-by-step explanation:
Formular for cube volumes:
since sides of a cube are identical:
Therefore:
but 1 mm³ = 0.000001 cm³
#1)
A) b = 10.57
B) a = 22.66
#2)
A) a = 1.35 (across from the 15° angle)
∠C = 50.07° (the angle at the top of the triangle)
∠B = 114.93°
B) ∠A = 83°
b = 10.77 (across from angle B)
a = 15.11 (across from angle A)
Explanation
#1)
A) Since b is across from the 25° angle and we have the hypotenuse, we have the information for the sine ratio (opposite/hypotenuse):
sin 25 = b/25
Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b
B) We will first use the cosine ratio. Side a is the side adjacent to the angle and we have the hypotenuse, and the cosine ratio is adjacent/hypotenuse:
cos 25 = a/25
Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a
Now we will use the Pythagorean theorem. We know from part a that side b = 10.57, and the figure has a hypotenuse of 25:
a²+(10.57)² = 25²
a² + 111.7249 = 625
Subtract 111.7249 from both sides:
a²+111.7249-111.7249=625-111.7249
a² = 513.2751
Take the square root of both sides:
√a² = √513.2751
a = 22.66
#2)
A) Let A be the 15° angle, B be the angle to the right and C be the angle at the top of the triangle. This means side a is across from angle A, side B is across from angle B, and side c is across from angle C.
Using the law of cosines,
a²=3²+4²-2(3)(4)cos(15)
a²=9+16-24cos(15)
a²=25-24cos(15)
a²=1.8178
Take the square root of both sides:
√a² = √1.8178
a = 1.3483≈1.35
Now we can use the Law of Sines to find angle C:
sin 15/1.35 = sin C/4
Cross multiply:
4*sin 15 = 1.35* sin C
Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin C)/1.35
(4*sin 15)/1.35 = sin C
Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin C)
sin⁻¹((4*sin 15)/1.35) = C
50.07 = C
To find angle B, add angle A and angle C together and subtract from 180:
B=180-(50.07+15) = 180-65.07 = 114.93
B) To find angle A, add angle B and angle C together and subtract from 180:
180-(52+45) = 180-97 = 83
Now use the Law of Sines to find side b (across from angle B):
sin 52/12 = sin 45/b
Cross multiply:
b*sin 52 = 12*sin 45
Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77
Find side a using the Law of Sines:
sin 83/a = sin 52/12
Cross multiply:
12*sin 83 = a*sin 52
Divide both sides by sin 52:
(12*sin 83)/(sin 52) = (a*sin 52)/(sin 52)
15.11 = a
8xy+65 take the 8 and multiply it to the 8 on the inside and that would be 64. 64 plus 1 is 65
Answer:
see attached
Step-by-step explanation:
<h3>1.</h3>
Solid dots go at all the end points except the one at (3, 6), which gets an open dot signifying the function is not defined for that point.
For the first portion of the graph, the square root function is shifted left one unit and scaled vertically by a factor of 3.
The second portion of the graph is a line with a slope of -1. It would have a y-intercept of 5 if it were defined there. It has an x-intercept of 5.
<h3>2.</h3>
The y-intercept is found by setting x=0 and solving for y.
... y = log(2·0+1) -1 = log(1) -1 = 0 -1 = -1
The x-intercept is found by setting y=0 and solving for x.
... 0 = log(2x +1) -1
... 1 = log(2x +1) . . . add 1
... 10 = 2x +1 . . . . . . take the antilog
... x = (10 -1)/2 = 4.5 . . . . . subtract 1, divide by the x coefficient
The intercepts are (0, -1) and (4.5, 0).
Answer:
6 teaspoons
Step-by-step explanation:
2 teaspoons = 1/3 tsp of salt
6 teaspoons = 1 tsp of salt
This was done by multiplying 2 by 3 since 3 thirds (3/3) make one whole.
So if 2 teaspoons are used for 1/3 teaspoon of salt, 4 teaspoons would be used for 2/3 teaspoon of salt and 6 teaspoons would be used for 1 teaspoon of salt.